i can't move music files to different folders in my itunes library

First, I have not created files in my itunes library for a while, and I could swear it was a lot easier years ago! ALL that I want to do is add the new music I've purchased or recently added to a folder that already exists in the playlist.

1) All my recently added songs have been purchased through my iphone, I'd like to move them to a folder.

2) When I connect my phone to my computer, I see the tab to click on my phone. I do, and it opens the content of Music in my iphone.

3) In this content, there are folders to the left listed, beginning with Music, Movies, Purchased, Recently Added, Recently Played, "My Name" Favorites, another specific folder I labeled to seperate music, and then another Purchased folder.

4) I WANT TO MOVE or copy my newly purchased music file to these folders so when I play them on my phone, I can SIMPLY choose the file that is asscoiated with my Favorites or other choice.

Why Is This So Difficult to do! Or is it that easy and I'm overlooking the past hour I've spent trying!

Second part of my aggravation, why can i NOT sort the files in a music folder by song name anymore?! We used to be able to click at the top of the listing, Name, Aritist, Albulm etc. to sort them alphabetically and make a search easier depending on , but now I can no longer do this.